In my experience the amount of priming sugar is not super critical (no pun intended). In other words, if you use 4 ounces or 5 ounces, it's not going to ruin your beer either way. I know that some people supposedly take the temperature of their beer and calculate the exact amount for the style (supposedly), but I've found that if you use roughly an ounce per gallon (roughly as in +/- 20%) of either dextrose or table sugar it will be fine.
I always boil the priming sugar in a couple cups of water and add it to the bottling bucket. I whirlpool gently with my racking cane. I just don't see how that's introducing any extra air.